Apparatus and method for processing a plurality of signals

ABSTRACT

A method for processing a plurality of signals, comprising the steps of: sampling n samples from each of a plurality of analog signals S i (t), multiplying by corresponded m×n linearly independent function groups  i a j (t), adding the resultants to establish the transformed signals S 0   i (t), summing all the transformed signals S 0   i (t) to produce a preliminary mixed signal SM(t); this preliminary mixed signal SM(t) being mathematically processed with the synchronous signal sin(qw 0 t) and the interruption cancellation signal sin(pw 0 t) which contains the basic angular frequency w 0  to establish a new signal SMS(t) for transmitting; wherein, SMS(t)=Sin(pw 0 t)×SM(t)+Sin(qw 0 t). In order to cancel interruptions during transmitting, the value of signal SMS(t) is zero at the boundaries of each time period. . In additions, the frequency range of the linearly independent signal  i a j (t) is between  
           A   i            T   1     v                   Hz     ∼       (         A   i            T   1     v       +       T   1       2      v         )                   Hz                 and                   A   i            T   1     v                   Hz     ∼       (         A   i            T   1     v       +       T   1       2      v         )                     Hz   .                     
 
     Moreover, to simplify the processing, appropriate intervals can be placed between every  i a j (t).

FIELD OF THE INVENTION

[0001] This invention relates to an apparatus and a method forprocessing a plurality of signals, more particularly, to an apparatusand method for processing a plurality of signals which cansimultaneously transmit a plurality of signals in a single transmissionline or channel and the bandwidth is invariant to the types or amount ofthe signals.

BACKGROUND OF THE INVENTION

[0002] In the present age, the need of the data transmitting efficiencygrows in an exponential rate. The lack of bandwidth is noticed in bothdigital and analogue data transmissions through both wired and wirelessmediums, such as in internets, broadcasting channels, and cell phones,

[0003] Traditionally, two methods were used to increase the datatransmitting capacity within a limited bandwidth. The first method isdividing a relatively wide bandwidth into several narrower bands so asto simultaneously transmit signals which have been pre-modulated intodifferent bandwidths. Examples of this first method are the signaltransmitting of traditional televisions and radios. Because hightechniques are required and interferences easily occur duringtransmitting, only limited number of channels are available via thisfirst transmitting method. Thus, the need of the bandwidth at thepresent age cannot be fulfilled.

[0004] The second method is cutting the plurality of signals into smallsegments and transmitting at different time under the same frequency.Segments of signal are reconnected at the receiving end. Datatransmitting of the traditional internet is an example. However, thissecond data-transmitting method has low efficiencies and frequentlyresulting in internet jam while simultaneously transmitting large amountof signals.

[0005] The U.S. Pat. No. 6,442,224 B1 (which pattern right has beentransferred to the inventor and is referred as Pat.224 hereafter)revealed a method and apparatus for mixing and separating a plurality ofsignals. As in the Pat. 224, linearly independent signals are separated,n samples (S_(i)(t_(j)), j=1,2, . . . n) are taken from each of theseparated m signals (S_(i)(t), i=1,2, . . . m). The n samples weremultiplied by linearly independent signals (such as m X n sets ofdifferent sinusoidal signals _(i)a_(j)(t)) and the products were summedto form a single mixed signal SM(t) for transmitting, wherein$\left. {{{S\quad {M(t)}} = {\sum\limits_{i = 1}^{m}\quad {S_{i}^{o}(t)}}},{{{and}\quad {S_{i}^{o}(t)}} = {\sum\limits_{j = 1}^{n}\quad \left\lbrack {S\quad {i\left( {t\quad j} \right)}i\quad a\quad {j(t)}} \right\rbrack}},{i = 1},2,\quad {\ldots \quad m}} \right).$

[0006] Transmitting this single mixed signal SM(t) requires only singlebandwidth which is the maximum bandwidth of the selected _(i)a_(j)(t).This single bandwidth is affected neither by the amount nor by thebandwidths of S_(i)(t). Therefore, a plurality of signals cansimultaneously be transmitted which resolving the problems about limitedbandwidth in the prior techniques.

[0007] However, there are still some problems in Pat. 224.

[0008] (1) In pat. 224, the signal SM(t) is transmitted and received insegments with the time period [T₀, T₁] of each segment. A synchronoussignal is transmitted first and followed by the main data signal SM(t)within each time period. At the receiving end, the main data signals arereceived after receiving the synchronous signal. Therefore, the timeperiod [T₀, T₁] as described in Pat. 224 has to be separated into twointervals [T₀, T₁′] and [T₁′, T₁] wherein T₀<T₁′<T₁. The interval [T₀,T₁′] is referred as synchronizing time period which is used fortransmitting the synchronous signal; whereas, the interval [T₁′, T₁] isreferred as data period which is used for transmitting the main datasignal SM(t). Consequently, the synchronizing time period causes a timedelay and the main data signal SM(t) is not able to complete the wholecycle within the time period [T₀, T₁]. Thus, interruptions of the maindata signal SM(t) may occur as described in FIG. 13.

[0009] (2) In Pat. 224, the method of selecting m x n sets of linearlyindependent signals ( such as sinusoidal signal _(i)a_(j)(t) ) is toequally cut the pre-determined bandwidth into several frequency bands toobtain signal _(i)a_(j)(t). This method is appropriate while in lowfrequency conditions. However, if in the high frequency conditions, thetwo consecutive frequency bands will be difficult to be separated andprocessed. For example, if the pre-determined maximum bandwidth is 4K Hzand will be cut into 100 bands, there will be a 40 Hz difference betweentwo consecutive frequency bands. In low frequency condition such as 40Hz versus 80 Hz, the signal is easy to be processed because 80 Hz istwice of 40 Hz. However, in high frequency condition such as 3600 Hzversus 3640 Hz, the frequency bands are almost overlapped and aredifficult to be separated.

[0010] (3) In Pat. 224. solving simultaneous equations is a requiredprocedure to separate mixed signals. However, the circuit for solvingsimultaneous equations is too huge and complicate to be designed. Theefficiency of this circuit is sub-optimal due to prolonged calculationtime. In additions, the total cost will rise.

[0011] Therefore, there is room for advancing the techniques revealed inPat. 224.

SUMMARY OF THE INVENTION

[0012] The first purpose of this invention is to provide a method andapparatus which can transmit mixed signals without interruptions withinall time periods and the value of the mixed signals are zero at theboundaries of each time period.

[0013] The second purpose of this invention is to provide a method andapparatus for processing a plurality of signals which can mix asynchronous signal into the main data signal, transmit this mixedsignal, and separate the synchronous signal at the receiving end. Theseparated synchronous signal is served as the time controller for thesubsequent processing. Therefore, this method can transmit signalswithin the whole time period [T₀, T₁], complete the cycles (period) ofthe signals within each of the time period and avoid the interruptionscaused by the intervals for transmitting synchronous signals asdescribed in Pat. 224.

[0014] The third purpose of this invention is to provide a method andapparatus for processing of a plurality of signals, wherein, within thefrequency range$\left( {{A_{i}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{i}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}} \right)$

[0015] of the linearly independent signal _(i)a_(j)(t), appropriateintervals are placed between two consecutive frequency bands and theinterval increased as the frequency increased so as to simplify thesubsequent processing.

[0016] The forth purpose of this invention is to provide a method andapparatus for processing a plurality of signals, through this method andthe circuit designed for implementing this method, solving homogeneousordinary difference equations and obtaining some constant values so thatthe simultaneously transmitted synchronous signal and each of thelinearly independent signals can be separated and reconstructed at thereceiving end.

[0017] The fifth purpose of this invention is to provide a method andapparatus for processing a plurality of signals, through this method andthe circuit designed for implementing this method, solving thehomogeneous ordinary differential equations and obtaining some constantvalues so that the simultaneously transmitted synchronous signal andeach of the linearly independent signals can be separated andreconstructed at the receiving end.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 is an embodiment of circuit blocks according to formula 4of this invention.

[0019]FIG. 2 is an embodiment of circuit blocks according to formula 5of this invention.

[0020]FIG. 3 is an embodiment of circuit blocks according to formula(6)-3 of this invention.

[0021]FIG. 4 is an embodiment of circuit blocks according to formula (8)of this invention.

[0022]FIG. 5 is an embodiment of circuit blocks according to formula(9)-1 of this invention.

[0023]FIG. 6, FIG. 7 and FIG. 8 are the diagrams of the circuit blocksfor separating the mixed signals at the receiving end.

[0024]FIG. 9 and FIG. 10 represent an embodiment of circuit blocksaccording to formula (12) of this invention.

[0025]FIG. 11 and FIG. 12 demonstrate an embodiment of circuit blocksfor processing a plurality of signal at the receiving end.

[0026]FIG. 13 is the potential output signal in the Pat. 224.

DETAILED DESCRIPTION OF THE INVENTION

[0027] The method of this invention comprising the steps of sampling insamples from each of a plurality of analog signals S_(i)(t), multiplyingby corresponded m X n sets of linearly independent function groups_(i)a_(j)(t), summing the resultants to establish transformed signals S⁰_(i)(t) and summing all the transformed signals S⁰ _(i)(t) to produce apreliminary mixed signal SM(t). This preliminary mixed signal SM(t) isnot transmitted right away but is mixed with a synchronous signalsin(qw₀t) and an interruption cancellation signal sin(pw₀t) whichcontains a basic angular frequency son, to establish a new signal SMS(t)for transmitting, wherein, SMS(t)=Sin(pw₀t)×SM(t)+Sin(qw₀t). Thetransmitted signal SMS(t) is continuous without interruptions because ofthe synchronous signal being mixed and transmitted simultaneously withthe main data signal, and the values of the transmitted signal beingzero at the boundaries of each time period. The plurality of signals canbe correctly separated at the receiving end. In additions, within thefrequency range$\left( {{A_{i}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{i}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}} \right)$

[0028] of the linearly independent signal _(i)a_(j)(t), appropriateintervals are placed between consecutive _(i)a_(j)(t) to simplify thesubsequent processing.

[0029] Follows are embodiments of this invention including detaildescriptions of the basic principle, processing methods and the possibleoutcome.

[0030] I. The basic principles of the mixing techniques at thetransmitting end.

[0031] (1) Methods described in Pat. 224

[0032] A plurality of signals S_(i)(t) is received within a time period[T₀,T₁], wherein i=1,2, . . . m, m is a positive integer, t is a timevariable and tε[T₀,T₁].

[0033] S_(i)(t_(j)), j1,2, . . . n, are samples which have been sampledfrom the corresponding S_(i)(t) within time period [T₀,T₁].

[0034] S_(i)(t) are multiplied by the corresponded predetermined m×nsets of the linearly independent function groups _(i)a_(j)(t) toestablished m sets of transformed signal S_(i) ⁰(t). S_(i) ⁰(t) can bemathematically represented as:${S_{i}^{0}(t)} = {\sum\limits_{j = 1}^{n}\quad \left\lbrack \quad {{{{}_{}^{}{}_{}^{}}(t)}{S_{i}\left( t_{j} \right)}} \right\rbrack}$

[0035] i=1,2, . . . m

[0036] The m sets of the transformed signal S⁰ _(i)(t) are summed toobtain a preliminary mixed signal SM(t). This procedure ismathematically represented as: $\begin{matrix}{{{S\quad {M(t)}} = {\sum\limits_{i = 1}^{m}\quad {S_{i}^{o}(t)}}};} & {< {{formula}\quad 1} >}\end{matrix}$

[0037] In Pat. 224, SM(t) is the signal to be transmitted to thereceiving end.

[0038] (2) In this invention, we provide an embodiment which can advancethe mixing technique as revealed in Pat. 224.

[0039] Let T₀ to be zero and the basic angular$w_{0} = {\frac{2\quad \pi}{T_{1}}.}$

[0040] The signal transmitted to the receiving end is:

SMS(t)=Sin(pw ₀ t)×SM(t)+Sin(qw ₀ t)  <formula 2>

[0041] Wherein ${P = \frac{r + 1}{2}},$

[0042] r can be a positive integer or zero; q can be $\frac{1}{2}$

[0043] or 1.

[0044] In formula 2, the values of signal SMS(t) are zero at theboundaries of every time period [0,T₁]. Therefore, interruptions asdescribed in Pat. 224 will not happen. In other words, interruptioncancellation signal Sin(pw₀t) can ensure the value of SMS(t) to be zeroat both the starting and ending points of each time period .

[0045] In formula 2, the synchronous signal Sin(qw₀t) is served as adiscriminating signal for discriminating each of the time periods. Theprecise point within each time period can be known by checking the valueof signal Sin(qw₀t). The method for precisely extracting signalSin(qw₀t) out of the mixed signals is presented else where in thisdocument. If ${q = \frac{1}{2}},$

[0046] every half cycle of Sin(qw₀t) represents the point of finishingthe previous time period and starting the subsequent time period.Whereas, if q=1, every full cycle of Sin(qw₀t) represents the point offinishing the previous time period and starting the following timeperiod.

[0047] An embodiment of this mixing technique requires the followinghardware:

[0048] At least a receiving unit, for receiving the signal S_(i)(t);

[0049] Several A/D converters, for sampling and digitizing the signalS_(i)(t);

[0050] Several signal generators, for generating signal _(i)a_(j)(t);

[0051] Several first multipliers, for calculating the product ofS_(i)(t_(j))×_(i)a(t), wherein, S_(i)(t_(j)) is the j^(th) sample ofS_(i)(t);

[0052] At least a first adder, for calculating${{{SM}(t)} = {\sum\limits_{i = 1}^{m}{S_{i}^{o}(t)}}};$

[0053] A synchronous signal generator, for generating a synchronoussignal sin(w₀t) within the time period [T₀,T₁];

[0054] At least a second multiplier and a second adder, calculatingSMS(t)=Sin(pw₀t)×SM(t)+Sin(qw₀t)

[0055] And a transmitter transmitting the processed mixed signal SMS(t).

[0056] (3) The second embodiment illustrates a better method to select_(i)a_(j)(t) in compared with that in Pat. 224.

[0057] This mixing technique can mix sound signals and comprise threesteps:

[0058] Step 1: Selecting the frequency range of _(i)a_(j)(t) to bebetween${{A_{i}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{i}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},$

[0059] wherein, A1 are positive integers including zero;

[0060] In other words, the frequency range of _(i)a_(j)(t) is between${{A_{1}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{1}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},$

[0061] the frequency range of ₂a_(j)(t) is between${{A_{2}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{2}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},$

[0062] and so forth; wherein, v is a positive integer.

[0063] Step 2: In formula 1, obtaining v samples from SM(t_(s)) (s=1,2,. . . v).

[0064] Step 3: Selecting additional v sets of function groups b_(v)(t)which are linear independent within the time period [0,T₁], establishingTSM(t) by formula 3: $\begin{matrix}{{{TSM}(t)} = {\sum\limits_{s = 1}^{v}\left\lbrack {{{SM}\left( t_{s} \right)}{b_{s}(t)}} \right\rbrack}} & {< {{formula}\quad 3} >}\end{matrix}$

[0065] Step 4: In order to mix the synchronous signal and eliminatepossible interruptions at the boundaries of each time period, the actualsignal received by the receiving unit is TSMS(t) which can bemathematically represented as:

TSMS(t)=sin(pw ₀ t)TSM+sin(qw ₀ t)  <formula (3)-1>

[0066] Wherein, p=(r+1)/2 , r can any positive integers including zero,q can be ½ or 1, and w₀=2π/T₁ .

[0067] In the second embodiment of this invention, the amount oftransmitted data is increased within a limited bandwidth.

[0068] This second embodiment requires the following hardware:

[0069] m sets of A/D converters, for sampling and digitizing signalS_(i)(t);

[0070] m×n signal generators, for generating signal _(i)a_(j)(t),wherein, the frequency range of the signal _(i)a_(j)(t) is${{A_{i}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{i}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},$

[0071] v=1,2, . . . m,;

[0072] m×n first multipliers, for calculating the product function ofS_(i)(t_(i))×_(i)a_(j)(t), wherein, S_(i)(t_(i)) is the j^(th) sample ofthe signal S(t);

[0073] At least a first adder, for calculating${{{{SM}(t)} = {\sum\limits_{i = 1}^{m}{S_{i}^{o}(t)}}};};$

[0074] A synchronous signal generator, for generating synchronous signalsin(w₀t) within the time period [T₀,T₁];

[0075] At least a converter, for sampling v samples from signal SM(t);

[0076] Several third signal generators, for generating v sets oflinearly independent function groups b_(s)(t);

[0077] At least a second multiplier and a second adder, for calculatingthe transformed signal TSM(t) of the signal SM(t_(s));

[0078] At least a second multiplier and a second adder, for calculatingthe mixed signal TSMS(t); and,

[0079] A transmitter transmitting processed mixed signal SMS(t).

[0080] II. Basic principles of separating the mixed signal at thereceiving end:

[0081] (1) Basic principle 1—solving homogenous ordinary differenceequations The solution of formula (4) is y_(k)=c₁cos kθ_(i)+c₂sinkθ_(i), wherein c₁ and c₂ are any constants.

y_(k−2)−2cos θ_(i) y _(k−1) +y _(k)=0  <formula (4)>

[0082] This behaves like a single frequency filter. Descriptions areprovided in the circuit blocks of FIG. 1. Hence, if the frequency of asignal is θ_(i), the value of this signal will become zero and befiltered out. By gradually varying the value of θ_(i), unwanted signalscan filtered out. An embodiment of formula 4 is described by the circuitblocks of FIG. 1. If the input is c₁ cos kθ_(i)+c₂ sin kθ_(i), theoutput is zero. In other words, input signals which contain angularfrequency θ_(i) are filtered out.

[0083] Utilizing S to represented the difference operator so thatformula 4 can be modified as formula (4)-1.

(S ⁻²−2cos θ_(i) S ⁻¹ +S ⁰)y _(k)=0  <formula (4)-1>

[0084] Formula 5 represents a difference equation of forth order

(S ⁻²−2cos θ_(i) S ⁻¹ +S ⁰)(S ⁻²−2cos θ₂ S ⁻¹ +S ⁰)y _(k)=0  <formula(5)>

[0085] Formula (5) can also be represented as:

[S ⁻⁴−2(cos θ₁+cos θ₂)S ⁻³+(4cos θ₁ cos θ₂+2)S ⁻²−2(cos θ₁+cos θ₂)S ⁻¹+S ⁰ ]y _(k)=0

[0086] Thus:

y _(k−4)−2(cos θ₁+cos θ₂)y _(k−3)+(4cos θ₁ cos θ₂+2)y _(k−2)−2(cosθ₁+cos θ₂)y _(k−1) +y _(k)=0  <formula(5)-1>

[0087] The solutions of the formula (5)-1 is y_(k)=coskθ_(i)+c₂sinkθ_(i)+c₃coskθ₂+c₄sink θ₂; c₁, c₂, c₃ and c₄ are constants.

[0088] An embodiment of formula 5 is described by the circuit blocks ofFIG. 2, wherein, input signals which contain the angular frequencies θ₁and θ₂ are filtered out.

[0089] Formula 6 is a ordinary difference equation of 2(n−1)^(th) order.$\begin{matrix}\left\lbrack \quad {{\prod\limits_{i = 1}^{u - 1}{\left( {S^{- 2} - {2\quad \cos \quad \theta_{i}S^{- 1}} + 1} \right) \cdot {\prod\limits_{i = {u + 1}}^{n}{\left( {S^{- 2} - {2\quad \cos \quad \theta_{i}S^{- 1}} + 1} \right\rbrack y_{k}}}}} = 0} \right. & {< {{formula}\quad (6)} >}\end{matrix}$

[0090] Formula (6) can be modified into formula (6)-1.

L _(u)(S)y _(k)=0  <formula (6)-1>

[0091] Wherein:${L_{u}(s)} = {\prod\limits_{i = 1}^{u - 1}{\left( {{S^{- 2}\cos \quad \theta_{i}S^{- 1}} + 1} \right) \cdot {\prod\limits_{i = {u + 1}}^{n}\left( {S^{- 2} - {2\quad \cos \quad \theta_{i}S^{- 1}} + 1} \right)}}}$

[0092] , n are positive integers.

[0093] Formula (6) and formula (6)-1 can further be modified intoformula (6)-2:

a _(u)(2n−2)y _(k−2n+2) +a _(u)(2n−3)y _(k−2n+3) +a _(u)(2n−5)y_(k−2n+4) + . . . +a _(u)(1)y _(k−1) +a _(u)(0)y _(k)=0  <formula (6)-2>

[0094] Wherein, a_(u)(v), v=0, 1, . . . 2n−2, are the coefficients ofS^(−v) after development of L_(u)(S).

[0095] Because both a_(u)(2n−2) and a_(u)(0) are equal 1, formula (6)-2can be modified into formula (6)-3:

y _(k−2n+2) +a _(u)(2n−3)y _(k−2n+3) +a _(u)(2n−4)y _(k−2n+4) + . . . +a_(u)(1)y _(k−1) +y _(k)=0  <formula (6)-3>

[0096] The circuit blocks of FIG. 3 represented an embodiment of formula(6)-3.

[0097] The solution of formula (6)-3 is:$y_{k} = {\sum\limits_{i = 1}^{u - 1}\left( {{C_{i}\cos \quad k\quad \theta_{i}} + {b_{i}\sin \quad k\quad \theta_{i}} + {\sum\limits_{i = {u + 1}}^{n}\left( {{C_{i}\cos \quad \theta_{i}} + {b_{i}\sin \quad k\quad \theta_{i}}} \right)}} \right.}$

[0098] ; C_(i) and b_(i) are constants.

[0099] Therefore, in FIG. 3, if the input signals are$\sum\limits_{i = 1}^{n}\left( {{{A_{i}\cos \quad k\quad \theta_{i}} + {B_{i}\sin \quad k\quad \theta_{i}}},} \right.$

[0100] all signals will be filtered out at point z of FIG. 3 exceptA_(u)cosk θ_(u)+B_(u)sink θ_(u). The value of Mu is $\begin{matrix}{M_{u} = {\frac{1}{2 \cdot {\prod\limits_{i = 1}^{u - 1}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}} \cdot \frac{1}{\prod\limits_{i = {u + 1}}^{n}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}}} & {< {{formula}\quad (7)} >}\end{matrix}$

[0101] At point z, because signal A_(u) ^(cos)kθ_(u)+B_(u) ^(sin)kθ_(u)is diminished to be $\frac{1}{M_{u}}$

[0102] of the original, it has to be multiplied by M_(u) to be theactual output.

[0103] An embodiment of the basic principle 1 for separating the mixedsignal at the receiving end requires the following hardware:

[0104] A receiving unit, for receiving processed mixed signals:

[0105] At least a sampling unit, for sampling 2n−1 samples from theprocessed mixed signal and the 2n−1 samples being mathematicallyrepresented as: y_(k−2n+2), y_(k−2n+3), . . . y_(k);

[0106] A signal generator, for generating 2n−3 pre-determined constantcoefficients, a_(u)(1), a_(u)(2), . . . a_(u)(2n−3); and

[0107] several multipliers and adders, for producing the followingoutput signals:

[y _(k−2n+2) +a _(u)(2n−3)y _(k−2n+3) +a _(u)(2n−4)y _(k−2n+4) + . . .+a _(u)(1)y _(k−1) +y _(k) ]*M _(u),

[0108] wherein,$M_{u} = {\frac{1}{2 \cdot {\prod\limits_{i = 1}^{u - 1}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}} \cdot {\frac{1}{\prod\limits_{i = {u + 1}}^{n}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)} \circ}}$

[0109] (2) Basic principle 2—solving the homogeneous ordinarydifferential equations:

[0110] Formula 8 is a homogeneous ordinary differential equation.,$\begin{matrix}{{\left( {D^{2} + w_{i}^{2}} \right){y(t)}} = 0} & {< {{formula}\quad (8)} >}\end{matrix}$

[0111] The solution of formula 8 is y(t)=C₁cos w_(i)t+C₂sin w_(i)t; C₁and C₂ are constants.

[0112] An embodiment of formula 8 is presented in the circuit blocks ofFIG. 4. Input signals which contain angular frequency w_(i) are filteredout.

[0113] Formula 9 is ordinary differential equation of 2(n−1)^(th) order.$\begin{matrix}{{\left\lbrack {\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right){\prod\limits_{i = {u + 1}}^{n}\left( {D^{2} + w_{i}^{2}} \right)}}} \right\rbrack {y(t)}} = 0} & {< {{Formula}\quad (9)} >}\end{matrix}$

[0114] Formula (9) can be represented as formula (9)-1:

[D ^(2n−1)+α_(u)(n−2)D ^(2n−4)+α_(u)(n−3)D ^(2n−6)+ . . . +α_(u)(1)D²+1]y(t)=0  <formula (9)-1>

[0115] wherein, α_(u)(j) are the coefficients of D^(2n−2j), j=1,2, . . ., n−2 after development of$\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right){\prod\limits_{i + u + 1}^{n}{\left( {D^{2} + w_{i}} \right).}}}$

[0116] Circuit blocks of FIG. 5 represent an embodiment of formula(9)-1. In FIG. 5, after inputting signal${\sum\limits_{i = 1}^{n}\left( {{C_{i}\cos \quad w_{i}t} + {d_{i}\sin \quad w_{i}t}} \right)},$

[0117] all signals will be filtered out at point z, except C_(u) cosw_(u)t+d_(u) sin w_(u)t, wherein, C_(i) and d_(i) are constants.

[0118] The value of N_(u) is represented in formula 10. $\begin{matrix}{N_{u} = {\frac{1}{\prod\limits_{i = 1}^{u - 1}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}*\frac{1}{\prod\limits_{i + 1}^{n}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}}} & {< {{formula}\quad (10)} >}\end{matrix}$

[0119] At the point z of FIG. 5, signal C_(u) cos w_(u)t+d_(u) sinw_(u)t is diminished to be $\frac{1}{N_{u}}$

[0120] of the original. Therefore, the signal C_(u) cos w_(u)t+d_(u) sinw_(u)t has to be multiplied by N, to be the actual output.

[0121] An embodiment of the basic principle 2 for separating the mixedsignal at the receiving end requires the following hardware:

[0122] A receiving unit, for receiving processed mixed signal;

[0123] Several differentiators, for calculating derivatives of thereceived processed mixed signal and obtaining the following values:D^(2n−2) y(t), D^(2n−4) y(t), . . . D² y(t) l wherein, D^(x) y(t)represented the x^(th) derivative of y(t);

[0124] A signal generator, for generating n−2 pre-determined constantcoefficients, α_(u)(1), α_(u)(2), . . . α_(u)(n−2); and

[0125] Several multipliers producing following output signals:

[D ^(2n−1)+α_(u)(n−2)D ^(2n−4)+α_(u)(n−3)D ^(2n−6)+ . . . +α_(u)(1)D²+1]*N _(u),

[0126] wherein, α_(u)(j) are the coefficients of D^(2n−2j), j=1,2, . . ., n−2, after development of${{\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right)\quad {\prod\limits_{i + u + 1}^{n}\left( {D^{2} + w_{i}} \right)}}};{and}},{N_{u} = {\frac{1}{\prod\limits_{i = 1}^{u - 1}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}*{\frac{1}{\prod\limits_{i + 1}^{n}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}.}}}$

[0127] (3) Basic principle 3—There are 6 steps for separating signalswhich coupled with the signal mixing techniques described above. Anembodiment is illustrated in the circuit blocks of FIG. 6, FIG. 7, andFIG. 8.

[0128] Step 1: selecting _(i)a_(j)(t) which contain either pure sin(w_(ij)t) or pure cos (w_(ij)t) sinusoidal signal, wherein, all w_(ij)are different positive integers.

[0129] Step 2: If c=½. extracting the synchronous signal sin (qw₀t) fromTSM(t) of formula 3 by the method described in FIG. 5. The steps ofextracting the synchronous signal are presented in (3), (4), and (5) ofFIG. 6.

[0130] Step 3: In formula (3), TSM(t) contains angular frequency qw₀,|pw₀±w_(s)| (s=1,2, . . . v). Using the methods described in FIG. 5,extracting signals SM(t₁)b₁(t), SM(t₂)b₂(t), . . . SM(t_(v))b_(v)(t)individually. Detail steps of extracting these signals are presented ill601˜60 v of FIG. 6.

[0131] Step 4: t_(r) is selected within the time period [T₀,T₁]. Each ofthe b_(s)(t_(r)) (s=1,2, . . . v) is divided by the correspondingb_(s)(t_(r)) to obtain SM(t₁), SM(t₂), . . . SM(t_(v)). These proceduresare presented in 621-622- . . . 62 v of FIG. 6. Before extracting theSM(t_(s)) (s=1,2, . . . v), timer 63 outputs a pulse at the time whent=t_(r) and the switch SW_(s) (s=1,2, . . . v) is turned ON. The outputof 601-602- . . . 60 v circuit blocks are fed into dividers 621-622- . .. 62 v, in respectively. The embodiment of this divider can be aresistance voltage divider.

[0132] Step 5: 711˜71 m of FIG. 7 is utilizing general sampling theory.step 6: as described in FIG. 8.

[0133] III. Illustration of a simple embodiment

[0134] (1) at the transmitting aspect:

[0135] 1. In formula (1), letting n=8 and m=5; $\begin{matrix}{{S_{i}^{0}(t)} = {\sum\limits_{j = 1}^{n}\left\lbrack {{{{}_{}^{}{}_{}^{}}(t)}{S_{i}\left( t_{j} \right)}} \right\rbrack}} \\{{{{SM}(t)} = {\sum\limits_{i = 1}^{m}{S_{i}^{o}(t)}}};}\end{matrix}$

[0136] 2. letting T₀=0 and T₁=10⁻³, thus, w₀=2000π; in formula 2,letting p=q=½

[0137] 3. selecting five different sound signals, S_(i)(t), t=1,2,3,4,5;

[0138] 4. letting w(u)=2[300+130(u−1)]π, selecting: $\begin{matrix}\begin{matrix}{{{{{}_{}^{}{}_{}^{}}(t)} = {{\cos\left\lbrack {{w\left( {i*\frac{j + 1}{2}} \right)}t} \right\rbrack}\quad \left( {{if}\quad j\quad {are}\quad {odd}\quad {numbers}} \right)}};} \\{{{{}_{}^{}{}_{}^{}}(t)} = {{\sin\left\lbrack {{w\left( {i*\frac{j}{2}} \right)}t} \right\rbrack}\quad \left( {{if}\quad j\quad {are}\quad {even}\quad {numbers}} \right)}}\end{matrix} & {< {{formula}\quad (11)} >}\end{matrix}$

[0139] Thus, SMS(t) of formula (2) is presented as: $\begin{matrix}{{{SMS}(t)} = {{{\sin \left( {1000\quad \pi \quad t} \right)}{\sum\limits_{i = 1}^{5}{\sum\limits_{j = 1}^{8}{{S_{i}\left( t_{i} \right)}{{{}_{}^{}{}_{}^{}}(t)}}}}} + {\sin \left( {1000\quad \pi \quad t} \right)}}} & {< {{formula}\quad (12)} >} \\{{Wherein},} & \quad \\{{{\sum\limits_{i = 1}^{5}{\sum\limits_{j = 1}^{8}{{S_{i}\left( t_{i} \right)}{{{}_{}^{}{}_{}^{}}(t)}}}} + {\sin \left( {1000\quad \pi \quad t} \right)}} =} & {< {{formula}\quad (12)\text{-}1} >} \\{\quad {\sum\limits_{i = 1}^{5}\left\lbrack {{{S_{i}\left( t_{1} \right)}{\cos \left( {{w(i)}t} \right)}} + {{S_{i}\left( t_{2} \right)}{\sin \left( {{w(i)}t} \right)}} +} \right.}} & \quad \\{\left. \quad {{{S_{i}\left( t_{3} \right)}{\cos \left( {{w\left( {2i} \right)}t} \right)}} + \ldots + {{S_{i}\left( t_{8} \right)}{\sin \left( {{w\left( {4i} \right)}t} \right)}}} \right\rbrack =} & \quad \\{\quad {{{S_{1}\left( t_{1} \right)}{\cos \left( {600\quad \pi \quad t} \right)}} + {{S_{1}\left( t_{2} \right)}{\sin \left( {600\quad \pi \quad t} \right)}} + \ldots +}} & {< {{formula}\quad (12)\text{-}2} >} \\{\quad {{{S_{1}\left( t_{8} \right)}{\sin \left( {1380\quad \pi \quad t} \right)}} + {{S_{2}\left( t_{1} \right)}{\cos \left( {1640\quad \pi \quad t} \right)}} +}} & \quad \\{\quad {{{S_{2}\left( t_{2} \right)}{\sin \left( {1640\quad \pi \quad t} \right)}} + \ldots + {{S_{2}\left( t_{8} \right)}{\sin \left( {2420\quad \pi \quad t} \right)}} +}} & \quad \\{\quad {{{S_{3}\left( t_{1} \right)}{\cos \left( {2680\quad \pi \quad t} \right)}} + {{S_{3}\left( t_{2} \right)}{\sin \left( {2680\quad \pi \quad t} \right)}} + \ldots +}} & \quad \\{\quad {{{S_{3}\left( t_{8} \right)}{\sin \left( {3460\quad \pi \quad t} \right)}} + {{S_{4}\left( t_{1} \right)}{\cos \left( {3720\quad \pi \quad t} \right)}} +}} & \quad \\{\quad {{{S_{4}\left( t_{2} \right)}{\sin \left( {3720\quad \pi \quad t} \right)}} + \ldots + {{S_{4}\left( t_{8} \right)}{\sin \left( {4500\quad \pi \quad t} \right)}} +}} & \quad \\{\quad {{{S_{5}\left( t_{1} \right)}{\cos \left( {4760\quad \pi \quad t} \right)}} + {{S_{5}\left( t_{2} \right)}{\sin \left( {4760\quad \pi \quad t} \right)}} + \ldots +}} & \quad \\{\quad {{S_{5}\left( t_{8} \right)}{\sin \left( {5540\quad \pi \quad t} \right)}}} & \quad\end{matrix}$

[0140] Therefore, formula 12 contains angular frequencies (1000±600)π,(1000±860)π, (1120±1000)π, . . . (5540±1000)π and 1000π. Except for thesinusoidal signal, sin(1000πt), which is served as the synchronoussignal, all others signals have the same amplitude as that of theoriginal sound signals. For example, the amplitude of cos[(1000±600)πt]is S₁(t₁); the amplitude of sin[(1000±600)πt] is S₁(t₂), . . . , and theamplitude of sin[(5540±1000)πt] is S₅(t₈)°

[0141] 5. FIG. 9 and FIG. 10 demonstrate an embodiment of formula (12)for the transmitting end. Wherein, the transmitting signal Tx of FIG. 10represents the signal SMS(t) which is the actual signal to betransmitted from the transmitting end. Because the details of mixingtechniques have been described previously in this invention, the purposeof this embodiment is merely to provide a uncomplicated example. Moredetail illustrations can also be referred to FIG. 9 and FIG. 10.

[0142] (2) at the receiving aspect:

[0143] The circuit blocks of FIG. 11 and FIG. 12 demonstrate inembodiment at the receiving end. Tr of FIG. 12 is the input signalreceived from the transmitting end. cl is the output of synchronoussignal which re-sets all the circuit blocks. Because the details ofmixing techniques have been described previously in this invention, thepurpose of this embodiment is merely to provide a uncomplicated example.More detail illustrations can also be referred to FIG. 11 and FIG. 12.

[0144] Although the present invention has been described with referenceto the preferred embodiment thereof, it will be understood that theinvention is not limited to the details thereof. Various substitutionsand modifications have suggested in the foregoing description, and otherwill occur to those of ordinary skill in the art. Therefore, all suchsubstitutions and modifications are intended to be embraced within thescope of the invention as defined ill the appended claim.

What the claim is:
 1. a method for processing a plurality of signals,comprising the steps of: (a). receiving a plurality of analog signalsS_(i)(t) within a time period [T₀,T₁], wherein i=1,2, . . . m, m ispositive integer, t is time variable and tε[T₀,T₁]; T₀, T₁ εR; (b).Sampling said plurality of analog signals S_(i)(t) within said timeperiod ε[T₀,T₁] and obtaining n samples S_(i)(t_(j)) for each analogsignal, wherein j=1,2, . . . n, n is positive integer, t_(j) ε[T₀,T₁];(c). Selecting m×n predetermined linearly independent groups_(i)a_(j)(t) and producing a transformed signal S⁰ _(j)(t), saidtransformed signal S⁰ _(i)(t) can be mathematically represented as${S_{i}^{0}(t)} = {\sum\limits_{j = 1}^{n}\left\lbrack {{{{}_{}^{}{}_{}^{}}(t)}{S_{i}\left( t_{j} \right)}} \right\rbrack}$

(d). summing all said transformed signal S⁰ _(i)(t) and establishing afirst mixed signal SM(t) which can be mathematically represented as${{{SM}(t)} = {\sum\limits_{i = 1}^{m}{S_{i}^{o}(t)}}};$

and (e). selecting a predetermined synchronous signal sin(w₀t) andgenerating a second mixed signal SMS(t) which can be represented asSMS(t)=Sin(pw_(o)t)×SM(t)+Sin(qw_(o)t); Wherein w₀ is basic angularfrequency and w₀, p, qεR, tε[T₀,T₁], sin(pw₀t) is an interruptioncancellation signal which can zeroing the initial value of each of thetime pulse of said second mixed signal SMS(t), and said second mixedsignal SMS(t) can become a continuous and interruption-free signal. 2.The method as in claim 1, wherein ${P = \frac{r + 1}{2}},$

q can be either ½ or 1 and $w_{0} = {\frac{2\quad \pi}{T_{1}}.}$


3. The method as in claim 1, further comprising: According to saidpredetermined linearly independent group _(i)a_(j)(t) and saidpredetermined synchronous signal sin(w₀t), obtaining 2n−3 constantcoefficients a_(u)(1), a_(u)(2), . . . a_(u)(2n−3) via resolvinghomogeneous ordinary difference equations; sampling said received secondmixed signal SMS(t) and acquiring one sample from each of the fixed timedelay and obtaining total of 2n−1 samples, said 2n−1 samples can bemathematically represented as: y_(k−2n+2), y_(k−2n+3), . . . y_(k); andprocessing said 2n−1 samples to obtain said proposed synchronous signal,said processing method can be mathematically represented as: [y_(k−2n+2) +a _(u)(2n−3)y _(k−2n+3) +a _(u)(2n−4)y _(k−2n+4) + . . . +a_(u)(1)y _(k−1) +y _(k) ]* M _(u), wherein,$M_{u} = {\frac{1}{2 \cdot {\prod\limits_{i = 1}^{u - 1}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}} \cdot {\frac{1}{\prod\limits_{i = {u + 1}}^{n}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}.}}$


4. The method as in claim 1 further comprising steps for extracting aproposed synchronous signal from said second mixed signal SMS(t):solving said predetermined linearly independent group _(i)a_(j)(t) andsaid predetermined synchronous signal sin(w₀t) with homogeneous ordinarydifferential equation method and obtaining n−2 values of constantcoefficients α_(u)(1), α_(u)(2), . . . α_(u)(n−2); In a time period,received said second mixed signal SMS(t) is mathematically representedas y(t), and using 2^(nd) order differentiators to obtain n−1derivatives of y(t), said n−1 derivatives being able to be representedas D^(2n−2)y(t), D^(2n−4)y(t), . . . D²y(t), wherein D^(x)y(t) is thex^(th) derivative of y(t); and Processing said n−1 derivatives andobtaining said proposed synchronous signal, said processing beingmathematically represented as: [D ^(2n−1)+α_(u)(n−2)D^(2m−4)+α_(u)(n−3)D ^(2n−6)+ . . . +α_(u)(1)D ²+1]*N _(u), whereinα_(u)(j) is the coefficient of D^(2n−2j), j=1,2, . . . , n−2, afterdevelopment of${\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right)\quad {\prod\limits_{i + u + 1}^{n}\left( {D^{2} + w_{i}} \right)}}},{{{and}\quad N_{u}} = {\frac{1}{\prod\limits_{i = 1}^{u - 1}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}*{\frac{1}{\prod\limits_{i + 1}^{n}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}.}}}$


5. The method of claim 1, further comprising steps of separating saidsecond mixed signal SMS(t): extracting said synchronous signal sin(qw₀t)by the method of claim 3, said synchronous signal sin(qw₀t) being usedas the time controlled signal for subsequent analysis; separatingsignals SM(t₁)sin(pw₀t), SM(t₂)sin(pw₀t), . . . SM(t_(v))sin(pw₀t) whichcontain said synchronous signal sin (qw₀t) by the method of claim 3.obtaining SM(t₁), SM(t₂), . . . SM(t_(v)) according to dividingsin(pw₀t) from SM(t₁)sin(pw₀t), SM(t₂)sin(pw₀t), . . .SM(t_(v))sin(pw₀t) respectively; transforming said signals SM(t₁),SM(t₂), . . . SM(t_(v)) into serial signals; because said predeterminedlinearly independent group _(i)a_(j)(t) is a sinusoidal and synchronoussignal, said method in claim 3 can be used to separate each ofS₁(t_(j))_(i)a_(j)(t), S₂(t_(j))₂a_(j)(t), S_(m)(t_(j))_(m)a_(j)(t),wherein, j=1,2 . . . n; and dividing each of S_(i)(t_(j))_(i)a_(j)(t),S₂(t_(j))₂a_(j)(t), S_(m)(t_(j))_(m)a_(j)(t) by corresponding_(i)a_(j)(t) in order to obtain S_(i)(t).
 6. The method as in claim 1,further comprising steps for separating said second mixed signal SMS(t):Using said method in claim 4 to separating said synchronous signalsin(qw₀t) which consequently becomes the controlling signal for thesubsequent analysis. Using said method in claim 4 to separating signalSM(t₁)sin(pw₀t), SM(t₂)sin(pw₀t), . . . SM(t_(v))sin(pw₀t) which containsaid synchronous signal sin(qw₀t), Obtaining SM(t₁), SM(t₂), . . .SM(t_(v)) according to Dividing sin(pw₀t) from SM(t₁)sin(pw₀t),SM(t₂)sin(pw₀t), . . . SM(t_(v))sin(pw₀t) in correspondingly;Transforming said signals SM(t₁), SM(t₂), . . . SM(t_(v)) into serialsignals; Because _(i)a_(j)(t) is a sinusoidal and synchronous signal,said method in claim 4 can be used to obtain S₁(t_(j))_(i)a_(j)(t),S₂(t_(j))₂a_(j)(t), S_(m)(t_(j))_(m)a_(j)(t), wherein j=1,2 . . . n; andSeparating S_(i)(t) according to Dividing _(i)a_(j)(t) fromcorresponding S₁(t_(j))_(i)a_(j)(t), S₂(t_(j))₂a_(j)(t),S_(m)(t_(j))_(m)a_(j)(t).
 7. A method for processing a plurality ofsignals, comprising the steps of: receiving said plurality of analogsignals within a time period [T₀,T₁], each of said analog signals beingable to be mathematically represented by an equation of S_(i)(t) withinthe time period [T₀,T₁], wherein i=1,2, . . . m, m is integer, t is timevariable, tε[T₀T, T₁], T₀, T₁εR; Sampling the analog signals S_(i)(t)within the time period [T₀,T₁] and obtain n samples for each signal,said samples being mathematically represented by S_(i)(t_(j)), wherein nis integer, j=1,2, . . . n , t_(j)ε[T₀,T₁]; selecting m×n predeterminedlinearly independent group _(i)a_(j)(t), establishing a transformedsignal S⁰ _(j)(t) in corresponding to S_(i)(t), S⁰ _(i)(t) being able tobe mathematically represented as:${{S_{i}^{0}(t)} = {\sum\limits_{j = 1}^{n}\left\lbrack {{{{}_{}^{}{}_{}^{}}(j)}{S_{i}\left( t_{j} \right)}} \right\rbrack}},$

wherein, the frequency of said _(i)a_(j)(t) is within${{A_{i}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{i}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},$

A_(i) are positive integers including zero; Summing all said transformedsignal S⁰ _(i)(t) to generate a first mixed signal SM(t) which can bemathematically represented as${{{SM}(t)} = {\sum\limits_{i = 1}^{m}{S_{i}^{o}(t)}}};$

sampling said first mixed signal SM(t) within the time period [T₀,T₁],and obtaining v samples, said v samples being mathematically representedas SM(t_(s)), wherein s=1,2, . . . v, and selecting v predeterminedlinearly independent groups b_(s)(t) and generating a transformed signalSM(t_(s)) in corresponding to a second mixed signal TSM(t) which can bemathematically represented as:${{TSM}(t)} = {\sum\limits_{s = 1}^{v}\left\lbrack {{{SM}\left( t_{s} \right)}{b_{s}(t)}} \right\rbrack}$

selecting a predetermined synchronous signal sin(w₀t), generating athird mixed signal TSMS(t) which can be mathematically represented as:TSMS(t)=sin(pw₀t)TSM+sin(qw₀t); wherein, w₀ is basic angular frequency,and w₀, p, qεR, tε[T₀,T₁].
 8. The method as in claim 7, wherein${P = \frac{r + 1}{2}},$

r is a positive integer including zero, q can be either ½ or 1, and$w_{0} = {\frac{2\quad \pi}{T_{1}}.}$


9. The method of claim 7 further comprising steps for extracting aproposed synchronous signal from said third mixed signal TSMS(t):solving said predetermined linearly independent group _(i)a_(j)(t) andsaid predetermined synchronous signal sin(w₀t) with homogeneous ordinarydifference equation method and obtaining 2n−3 values of constantcoefficients a_(u)(1), a_(u)(2), . . . a_(u)(2n−3); Sampling saidreceived third mixed signal TSMS(t), getting one sample everypredetermined time delay within a time period and obtaining total of2n−1 samples, said 2n−1 samples being able to be mathematicallyrepresented as y_(k−2n+2), y_(k−2n+3), . . . y_(k); and Processing said2n−1 samples and producing said proposed synchronous signal, saidprocessing method being able to be mathematically represented as: [y_(k−2n+2) +a _(u)(2n−3)y _(k−2n+3) +a _(u)(2n−4)y _(k−2n+4) + . . . +a_(u)(1)y _(k−1) +y _(k) ]* M _(u), wherein$M_{u} = {\frac{1}{2 \cdot {\prod\limits_{i = 1}^{u - 1}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}} \cdot {\frac{1}{\prod\limits_{i = {u + 1}}^{n}\left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}.}}$


10. The method as in claim 7 further comprising steps for extracting aproposed synchronous signal from said third mixed signal TSNMS(t):solving said predetermined linearly independent group _(i)a_(j)(t) andsaid predetermined synchronous signal sin(w₀t) with homogeneous ordinarydifferential equation method and obtaining n−2 values of constantcoefficients α_(u)(1), α_(u)(2), . . . α_(u)(n−2); In a time period,received said third mixed signal TSMS(t) is mathematically representedas y(t), and using 2^(nd) order differentiators to obtain n−1derivatives of y(t), said n−1 derivatives being able to be representedas D^(2n−2)y(t), D^(2n−4)y(t), . . . D²y(t), wherein D^(x)y(t) is thex^(th) derivative of y(t); and Processing said n−1 derivatives andobtaining said proposed synchronous signal, said processing method beingable to be mathematically represented as: [D ^(2n−1)+α_(u)(n−2)D^(2n−4)+α_(u)(n−3)D ^(2n−6)+ . . . +α_(u)(1)D ²+1]*N _(u) whereinα_(u)(j) is the coefficient of D^(2n−2j) j=1,2, . . . , n−2, afterdevelopment of${\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right)\quad {\prod\limits_{i + u + 1}^{n}\left( {D^{2} + w_{i}} \right)}}},{and},{N_{u} = {\frac{1}{\prod\limits_{i = 1}^{u - 1}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}*{\frac{1}{\prod\limits_{i + 1}^{n}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}.}}}$


11. The method of claim 7 further comprising steps for separating saidthird mixed signal TSMS(t): extracting said synchronous signal sin(qw₀t)by the method of claim 9, said synchronous signal sin(qw₀t) being usedas the time controlled signal for subsequent analysis; Separatingsignals SM(t₁)b₁(t), SM(t₂)b₂(t), . . . SM(t_(v))b_(v)(t) which containsynchronous signals b_(v)(t) by the method of claim 9; obtaining SM(t₁),SM(t₂), . . . , SM(t_(v)) signals according to dividing b_(s)(t_(r))from SM(t₁)b_(s)(t_(r)), SM(t₂)b_(s)(t_(r)), . . . SM(t_(v))b_(s)(t_(r))in respectively; Transforming said SM(t₁), SM(t2), . . . , SM(t_(v))signals into serial signals; Using m band pass filters to filter saidserial signals, wherein the band width of each of said m band passfilters is from${{A_{v}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{v}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},{v = 1},2,{{\ldots \quad m};}$

Using the methods of claim 9 to separate each of theS₁(t_(j))_(i)a_(j)(t), S₂(t_(j))₂a_(j)(t), . . . ,S_(m)(t_(j))_(m)a_(j)(t), j=1,2, . . . , n; and Dividing each ofS₁(t_(j))_(i)a_(j)(t), S₂(t_(j))₂a_(j)(t), . . . ,S_(m)(t_(j))_(m)a_(j)(t) by the corresponding _(i)a_(j)(t) to obtainS_(i)(t).
 12. The method of claim 7 further comprising steps forseparating said processed mixed signal TSMS(t): extracting saidsynchronous signal sin(qw₀t) by the method of claim 10, said synchronoussignal sin(qw₀t) being used as the time controlled signal for subsequentanalysis; Separating signals SM(t₁)b₁(t), SM(t₂)b₂(t), . . .SM(t_(v))b_(v)(t) which contain synchronous signals b_(v)(t) by themethod of claim 10; obtaining SM(t₁), SM(t₂), . . . , SM(t_(v)) signalsaccording to dividing b_(s)(t_(r)) from SM(t₁)b_(s)(t_(r)),SM(t₂)b_(s)(t_(r)), . . . SM(t_(v))b_(s)(t_(r)), in respectively;Transforming said signals SM(t₁), SM(t₂), . . . , SM(t_(v)) into serialsignals; Using m band pass filters to filter said serial signals,wherein, the band width of each of said m band pass filters is from${{A_{v}\frac{T_{1}}{v}\quad {Hz}} \sim {\left( {{A_{v}\frac{T_{1}}{v}} + \frac{T_{1}}{2v}} \right)\quad {Hz}}},$

v=1,2, . . . m; Using the methods of claim 10 to separate each of theS₁(t_(j))_(i)a_(j)(t), S₂(t_(j))₂a_(j)(t), . . . ,S_(m)(t_(j))_(m)a_(j)(t), j=1,2 . . . n; and Dividing each of theS₁(t_(j))_(i)a_(j)(t), S₂(t_(j))₂a_(j)(t), . . . ,S_(m)(t_(j))_(m)a_(j)(t) by the corresponding _(i)a_(j)(t) to obtainS_(i)(t) .
 13. An apparatus for processing a plurality of signalsS_(i)(t), said apparatus comprising: at least a receiving unit, forreceiving said plurality of signals S_(i)(t) a plurality of A/Dconverters, for sampling and digitizing said plurality of signalsS_(i)(t) a plurality of signal generators, for generating linearlyindependent signals _(i)a_(j)(t); a plurality of first multipliers, forcalculating the product functions of S_(i)(t_(j)) multiplying by_(i)a_(j)(t), wherein S_(i)(t_(j)) is the j^(th) sample of saidplurality of signals S_(i)(t); at least a first adder, for calculating afirst mixed signal SM(t), wherein${{{SM}(t)} = {\sum\limits_{i = 1}^{m}\quad {S_{i}^{o}(t)}}};$

a synchronous signal generator, for generating a synchronous signalsin(w₀t), within said time period [T₀,T₁]; and at least a secondmultiplier and second adder, for calculating a second mixed signalSMS(t), wherein SMS(t)=Sin(pw₀t)×SM(t)+Sin(qw₀t).
 14. The apparatus asin claim 13, further comprising a transmitter for transmitting saidsecond mixed signal SMS(t).
 15. The apparatus as in claim 14, furthercomprising a receiver for receiving said second mixed signal SMS(t),said receiver comprising: at least a sampling unit, for sampling 2n−1samples from said second mixed signal SMS(t), said samples being able tobe mathematically represented as: y _(k−2n+2) , y _(k−2n+3) , . . . y_(k); a signal generator, for producing 2n−3 predetermined constantcoefficients a_(u)(1), a_(u)(2), . . . a_(u)(2n−3); and a plurality ofmultipliers and adders, for producing an output signal: [y _(k−2n+2) +a_(u)(2n−3)y _(k−2n+3) +a _(u)(2n−4)y _(k−2n+4) + . . . +a _(u)(1)y_(k−1) +y _(k) ]* M _(u), wherein$M_{u} = {\frac{1}{2 \cdot {\prod\limits_{i = 1}^{u - 1}\quad \left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}} \cdot {\frac{1}{\prod\limits_{i = {u + 1}}^{n}\quad \left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}.}}$


16. The apparatus as in claim 14, further comprising a receiver forreceiving said second mixed signal SMS(t), said receiver comprising: aplurality of differentiators, for calculating derivatives of said secondmixed signal SMS(t) and obtaining n−1 derivatives D^(2n−2) y(t),D^(2n−4) y(t), . . . D² y(t), wherein D^(x) y(t) is the x^(th)derivative of y(t); A signal generator, for producing n−2 predeterminedconstant coefficients α_(u)(1), α_(u)(2), . . . α_(u)(n−2) ; and Aplurality of multipliers and adders, for producing an output signal:[D^(2n−1)+α_(u)(n−3)D^(2n−4)+α_(u)(n−3)D^(2n−6)+ . . . +α_(u)(1)D²+1]*N_(u), wherein α_(u)(j) are coefficients of D^(2n−2j) j=1,2, . . . , n−2after development of${{\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right){\prod\limits_{i + u + 1}^{n}\quad \left( {D^{2} + w_{i}} \right)}}};{and}}\quad$$N_{u} = {\frac{1}{\prod\limits_{i = 1}^{u - 1}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}*{\frac{1}{\prod\limits_{i + 1}^{n}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}.}}$


17. An apparatus for using the method according to claim 7, saidapparatus comprising: m A/D converters, for sampling and digitizing saidplurality of signals S_(i)(t); m×n signal generators, for producing saidlinearly impendent signal _(i)a_(j)(t); wherein the frequency range of_(i)a_(j)(t) is${{A_{i}\frac{T_{1}}{v}H\quad z} \sim {\left( {{A_{i}\frac{T_{1}}{v}} + \frac{T_{1}}{2\quad v}} \right)H\quad z}},$

v=1,2, . . . m, said synchronous signals being mathematicallyrepresented as sin(w₀t); m×n first multipliers, for calculating theproduct function of S_(i)(t_(j)) multiplying by _(i)a_(j)(t), whereinS_(i)(t_(j)) is the j^(th) sample of S_(i)(t); at least a first adder,for calculating a mixed signal SM(t), wherein${{{SM}(t)} = {\sum\limits_{i = 1}^{m}\quad {S_{i}^{o}(t)}}};$

a synchronous signal generator, for producing synchronous signals withina time period [T₀,T₁]; at least a converter, for sampling v samples fromSM(t); a plurality of third signal generators producing v lineallyindependent function groups b_(s)(t); at least a second multiplier andsecond adder, for calculating said second mixed signal TSM(t) of saidmixed signal SM(t_(s)); and at least a third multiplier and third adder,for calculating said third mixed signal TSMS(t).
 18. The apparatus as inclaim 17, further comprising a transmitter for transmitting said thirdmixed signal TSMS(t)
 19. The apparatus as in claim 17, furthercomprising a receiver for receiving said third mixed signal TSMS(t),said receiver comprising: at least a sampling unit for sampling 2n−1samples from said third mixed signal TSMS(t), wherein said samples aremathematically represented as y _(k−2n+2) , y _(k−2n+3) , . . . y _(k);a signal generator producing 2n−3 constant coefficients a_(u)(1),a_(u)(2), a_(u)(2n−3) ; and a plurality of multipliers and adders, forproducing an output signal, said output signal being able to bemathematically represented as [y _(k−2n+2) +a _(u)(2n−3)y _(k−2n+3) +a_(u)(2n−4)y _(k−2n+4) + . . . +a _(u)(1)y _(k−1) +y _(k) ]* M _(u),wherein$M_{u} = {\frac{1}{2 \cdot {\prod\limits_{i = 1}^{u - 1}\quad \left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}} \cdot {\frac{1}{\prod\limits_{i = {u + 1}}^{n}\quad \left( {{\cos \quad \theta_{u}} - {\cos \quad \theta_{i}}} \right)}.}}$


20. The apparatus as in claim 17, further comprising a receiver forreceiving said third mixed signal TSMS(t), said receiver comprising: aplurality of differentiators, for calculating derivatives of said thirdmixed signal TSMS(t) and obtaining n−1 derivatives D^(2n−2)y(t),D^(2n−4)y(t), . . . D²y(t), wherein D^(x)y(t) is the x^(th) derivativeof y(t); A signal generator, for producing n−2 predetermined constantcoefficients α_(u)(1), α_(u)(2), . . . α_(u)(n−2); and A plurality ofmultipliers and adders producing an output signal [D ^(2n−1)+α_(u)(n−1)D^(2n−4)+α_(u)(n−3)D ^(2n−6)+ . . . +α_(u)(1)D ²+1]*N _(u), whereinα_(u)(j) are coefficients of D^(2n−2j) after development of${{\prod\limits_{i = 1}^{u - 1}{\left( {D^{2} + w_{i}^{2}} \right){\prod\limits_{i + u + 1}^{n}\quad \left( {D^{2} + w_{i}} \right)}}},{j = 1},2,\quad \ldots \quad,{n - 2},{and}}\quad$$N_{u} = {\frac{1}{\prod\limits_{i = 1}^{u - 1}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}*{\frac{1}{\prod\limits_{i + 1}^{n}\left( {{- w_{u}^{2}} + w_{i}^{2}} \right)}.}}$